Calvin Klein’s on-off boy toy Nick Gruber has been questioned by cops after he was involved in a bloody fight at a top Hamptons nightclub.

Matt Rich, a spokesman for Gruber, confirmed that the model and former porn star went to East Hampton Police Station on Friday at 8:30 a.m. to answer questions about the July 20 dust-up.

Rich said, “Police saw my name in the Page Six story about the fight, and called me on Wednesday to say they wanted to interview Nick. He voluntarily . . . spoke with the police for an hour, it was a friendly conversation, and he was not arrested.”

We are told that Nick plans to file a complaint of sexual assault following the early hours incident at hot club SL East, as he says the altercation began when a stranger randomly grabbed his crotch.

Spies said Gruber, who had begun his night at Sienna and Pink Elephant, then hit the clubgoer, “causing a laceration over his right eye.” But after Gruber and the guy were taken outside, Gruber allegedly threw an SL security guard to the ground and ran. An ambulance was called for the unnamed guy, who had blood gushing from his head.

“It was a blood bath,” Pink Elephant director of VIP relations Artin Bey Archer told us at the time.“The [other] guy had blood all over his face. I saw him on the ground, and he was . . . taken away in an ambulance. Nick left before around six police cars arrived. Around 20 police officers started a full-scale manhunt . . . using [flashlights] to search through the bushes.” Two SL busboys were seen mopping up blood after the incident.

Gruber — who we are told is not back together with Klein despite the pair taking a Mexican vacation together recently — denied fleeing the scene, claiming he left after club security ordered him to leave.

A spokesperson for East Hampton Police was not available for comment.

Rich added, “Nick’s record was checked , and he fully cooperated with all aspects of routine processing. He was given a desk appearance ticket to come back to tell his story with his witnesses on Sept. 26 . . . Of course he’ll continue to cooperate fully. His lawyer is Michael McClellan.”